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Adept values and hand calculations do not match

In the n AlGaAs-pGaAs heterojunction example, the potential values do not seem to match with my hand calculations. If I use the formula for Vbi and then use that to calculate the VJn and VJp (potential drops on the n AlGaAs side and p GaAs side respectively), I get the following values 0.713 V and 0.660 V.

In Adept (at equilibrium, Va=0 V ), the potential value at x=0 um (on the AlGaAs side) is 0.55 V and at x = 1um is -0.81 V. The value at x =0.5 um is -0.15 V. Using these values one can get the potential drops for the n and the p sides as in the hand calculation above.

My question is , how did we get this value at x= 0.5 um for the voltage in the first place. I think that this has to do with choosing a reference material for this system (like in Dr Lundstrom’s heterojunction lectures). But, if I choose GaAs as the reference material I am unable to get the same values as ADEPT calculates for the potential. I am using the following expression (Eqn 44 in Dr Lundstrom’s heterostructure fundamentals notes) for the potential on the p GaAs side.

Vp= (Chi(x)-Chiref)-(Eg(x)-Egref)+kT*log(Nv(x)/Nvref).

If you plug in values for Chiref, Egref and Nvref by using GaAs as the reference material, Vp evaluates to 0 and the only potential drop we get is due to the doping (kT*log NA/ni_GaAs).

I am not sure how to go about reproducing the ADEPT solution with some hand calculations to convince myself.

Thanks for your help on this..

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    John Robert Wilcox

    I believe the first two paragraphs of the question refute the title. The built-in voltage and band offsets match the hand calculated values. (Please see pages 4-6 of the Heterostructure Tutorial for more information.)

    The problem appears to arise while attempting to calculate the absolute potential values, assuming GaAs parameters are used for the reference values Chi_ref, Eg_ref, … . In the numerical model the absolute value of the potential is not important, because the solution is calculated relate to the rest of the device.

    The reference parameters as outlined in Dr. Lundstrom’s heterostructure papers (DOI: 10.1109/T-ED.1983.21271, 10.1016/0038-1101(82)90195-2 and 10.1016/0038-1101(81)90082-4) are a straight forward way to include things such as band offset and doping effects in numerical calculations.

    The default reference parameters in ADEPT are:

    Nc_ref= 1.0000000000000D+19 Nv_ref= 1.0000000000000D+19 Eg_ref= 1.0000000000000 chi_ref= 4.0000000000000 ks_ref= 1.0000000000000 ni_ref= 35552099801.694

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    Xufeng Wang

    Potentials are relative to a certain reference, and I do believe this reference in ADEPT is chosen to be convenient for numerical calculation, and that’s why it seems the vacuum level starts at some non-zero value from the left side of the device. I’ll see if I can find some more details about the choice of reference from creators of this programs.

    Nice question, and I hope you are enjoy using ADEPT!

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